Question:
I have a question related to a PCA. It involves the target or desired value and projected forecast:
- The PCA gives excellent PC Values, but they are centered around zero since they are standardized.
- All desired/target values are positive since the markets only have positive values.
Here's what I've done so far: I've modeled and created a forecast for each variable separately using the PC values time series. Next, I computed each input variable's standardized corresponding values Using the loadings (weights) and the PC forecast values.
I'm trying to figure out how to transform standardized predicted values back to non-standardized forms. Are there specific Excel functions that could help with this process?
Answer:
The process of standardization entails subtracting the mean and then dividing the result by the standard deviation.
$$y_i = \frac{x_i - \bar{x}}{s}$$
To reverse the effect:
$$ x_i = y_i \times s + \bar{x}$$
- Compute each series's average ($\bar x$) and the standard deviation ($s$).
- Multiply the forecast value (in the standardized form) by the standard deviation (step 1).
- Add the average (computed in step 1) to the product (computed in step 2).
The above-outlined calculations should resolve the scaling (de-standardization) issue. You can do this in Excel using the STDEV(.) and AVERAGE(.) functions.
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